Next, we aim to explain the validity of the hole formation mechanism as a result of liquid film thinning.
Our numerical method does not consider the destabilising effect brought about by the van der Waals attractive forces as the film thickness tends to zero. [1]} reported that while the thinning takes place, the dynamics of the film enters into an asymptotic behaviour leading to its rupture, depending only on a balance between viscous, van der Waals, and surface tension forces. After the film puncture, the circular hole expansion is driven by capillarity, and fluid is accumulated in a circular rim which grows in size as it moves away from the puncture point. The retraction speed, \(V_{TC}\)  can be estimated by the classical `Taylor-Culick' theory, \(V_{TC}= (2 \sigma /\rho h)^{1/2} \) , where \(h\)  is the film thickness. Prior to the puncture \(h \sim 40 ~\mu \) m, giving an estimate of the retraction velocity as \(V_{TC} \sim 1.2\)  m/s. The measured retraction speed of the holes in our simulations ranges from \(0.75\)  m/s to \(1.2\)  m/s. This ensures that although our simulations cannot predict the exact location of the puncture, and their formation is mesh-dependent, its expansion is well predicted, ensuring that the physics is fully-resolved following the formation of the hole.
Additionally, the film thickness of the sheet prior to its rupture is on the order of \(h \sim 10^{-6}\)  m, which agrees with the findings of [2]}, [3]}, and [4]} who observed interface rupture for film sheets of the same order of magnitude.
